putnam-v1 / putnam-1965-a4

putnam-1965-a4

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1965-a4

What it runs

The Lean statement the swarm must prove — kernel-verified at Gate A. The trailing sorry is the open obligation a proof replaces.

goals/putnam-1965-a4.lean

import Mathlib

open EuclideanGeometry Topology Filter Complex

theorem putnam_1965_a4 {G B : Type*}
[Fintype G] [Nonempty G]
[Fintype B] [Nonempty B]
(dances : G → B → Prop)
(h : (¬∃ b : B, ∀ g : G, dances g b) ∧ ∀ g : G, ∃ b : B, dances g b)
: ∃ g h : G, ∃ b c : B, dances g b ∧ dances h c ∧ ¬dances h b ∧ ¬dances g c := by
  sorry

Runs (0)

No runs recorded for this suite yet — they appear here as the swarm attempts the benchmarks.